The Core0 C6 counter is really zero, so it looks like that core was never in C6 state (during your run-time).
When a counter is 0, it's not possible to know whether it's present or just didn't count anything yet, so it's not shown in HWiNFO. If you Core0 enters C6 state, the counter will start counting and it will appear in HWiNFO.